Bundle formations kinetics

In the perspective discussed in the present contribution, bundle formation occurs within the amorphous phase and in undercooled polymer solutions. It does not imply necessarily a phase separation process, which, however, may occur by bundle aggregation, typically at large undercoolings [mode (ii)]. In this case kinetic parameters relating to chain entanglements and to the viscous drag assume a paramount importance. Here again, molecular dynamics simulations can be expected to provide important parameters for theoretical developments in turn these could orient new simulations in a fruitful mutual interaction. 

The analysis above appears to contradict the experimental finding of a well-defined finite bundle size. We argue that the experimental observation is not an equilibrium effect, and that the kinetics of bundle formation lead to a well-defined size. In fact, we believe that the competition of the short-range attraction and longer range repulsion leads to unique kinetics of bundle growth [47]. 

The possible fatigue failure mechanisms of SWCNT in the composite were also reported (Ren et al., 2004). Possible failure modes mainly include three stages, that is, splitting of SWCNT bundles, kink formation, and subsequent failure in SWCNTs, and the fracture of SWCNT bundles. As shown in Fig. 9.12, for zigzag SWCNT, failure of defect-free tube and tubes with Stone-Wales defect of either A or B mode all resulted in brittle-like, flat fracture surface. A kinetic model for time-dependent fracture of CNTs is also reported (Satapathy et al., 2005). These simulation results are almost consistent with the observed fracture surfaces, which can be reproduced reasonably well, suggesting the possible mechanism should exist in CNT-polymer composites. 

The first term on the right-hand side is identical with that of Eq. (41) (since the nuclear kinetic energy cancel the Hamiltonian matrix Hrnn can be replaced by the PES matrix Vrnn, Eq. (10)). The derivatives in the second term on the right-hand side of Eq. (48) are responsible for the formation of a nuclear coordinate and momentum dependence of the density matrix. The multitude of involved coordinates and momenta, however, avoids any direct calculation of the pmn(R, / /,), and respective applications finally arrive at a computation of bundles of nuclear trajectories which try to sample the full density matrix. 

Kinetics is another important factor in determining if a mixture of nanoparticles and polymer can form a nanocomposite. The extent of nanoparticle dispersion (e.g., exfoliation of the stacks of clay platelets, debonding of nanotube bundles, and deagglomeration of nanosphere agglomerates) in a polymer matrix is affected critically by the kinetic barriers. Such kinetic barriers often inhibit the formation of thermodynamically favorable structure. 

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